The lock-up control of the automatic transmission aims at reducing a power loss by the torque converter at a high speed time by engaging the lock-up clutch in response to a vehicle speed, a depressed amount of an accelerator and the like at a predetermined shift range (in general, at a high speed range, for example, at the third speed,) so that an engine output shaft is directly coupled to an input shaft of the transmission mechanism without transmitting through the torque converter. Conventional lock-up control apparatus comprises a solenoid valve which is used exclusively for the lock-up control in addition to shift valves for the transmission mechanism. As the consequence, the constitution of the apparatus becomes complicated and the number of solenoid valves increases, also resulting in a high manufacturing cost of the apparatus. In connection with these points, there is much desired to be improved in the apparatus.